研究预测模型如何影响真实数据分布，揭示了性能优化带来的意外副作用。
On the Impact of Performative Risk Minimization for Binary Random Variables
- 针对二值变量设计序列化性能风险最小化框架
- 发现性能优化可能放大对数据分布的负面影响
- 适用于关注模型部署后社会效应的研究者
表现性（Performativity）指预测结果会反作用于实际数据分布，尤其在个体策略性响应的社交场景中尤为显著。为应对因表现性导致的分布漂移，Perdomo 等人（2020）提出性能风险最小化（PRM）框架以维持模型准确性。然而，该框架忽略了 PRM 对底层分布及预测结果的影响。本文首次系统分析了 PRM 的影响，研究具有二值随机变量和线性表现性漂移的序列化性能风险最小化问题。我们提出了两种自然的影响力度量，在完全信息情形下推导出 PRM 解与影响力度量的显式公式；在部分信息情形下，设计了表现性感知的统计估计器并进行仿真验证。分析表明，相较于不建模数据漂移的方法，PRM 可能产生更显著的副作用。
原文摘要 · Abstract (English)
Performativity, the phenomenon where outcomes are influenced by predictions, is particularly prevalent in social contexts where individuals strategically respond to a deployed model. In order to preserve the high accuracy of machine learning models under distribution shifts caused by performativity, Perdomo et al. (2020) introduced the concept of performative risk minimization (PRM). While this framework ensures model accuracy, it overlooks the impact of the PRM on the underlying distributions and the predictions of the model. In this paper, we initiate the analysis of the impact of PRM, by studying performativity for a sequential performative risk minimization problem with binary random variables and linear performative shifts. We formulate two natural measures of impact. In the case of full information, where the distribution dynamics are known, we derive explicit formulas for the PRM solution and our impact measures. In the case of partial information, we provide performative-aware statistical estimators, as well as simulations. Our analysis contrasts PRM to alternatives that do not model data shift and indicates that PRM can have amplified side effects compared to such methods.
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